{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c8d25fe2",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "# Optional Lab: Feature scaling and Learning Rate (Multi-variable)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8b967e2",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Goals\n",
    "In this lab you will:\n",
    "- Utilize  the multiple variables routines developed in the previous lab\n",
    "- run Gradient Descent on a data set with multiple features\n",
    "- explore the impact of the *learning rate alpha* on gradient descent\n",
    "- improve performance of gradient descent by *feature scaling* using z-score normalization"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3dfbbe3c",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Tools\n",
    "You will utilize the functions developed in the last lab as well as matplotlib and NumPy. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "1a086458",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from lab_utils_multi import  load_house_data, run_gradient_descent \n",
    "from lab_utils_multi import  norm_plot, plt_equal_scale, plot_cost_i_w\n",
    "from lab_utils_common import dlc\n",
    "np.set_printoptions(precision=2)\n",
    "plt.style.use('./deeplearning.mplstyle')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "914339ff",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Notation\n",
    "\n",
    "| General Notation | Description | Python (if applicable) |\n",
    "|:----------------:|:-----------:|:----------------------:|\n",
    "|      $a$         | scalar, non-bold | |\n",
    "|  $\\mathbf{a}$   | vector, bold | |\n",
    "|  $\\mathbf{A}$   | matrix, bold capital | |\n",
    "| **Regression** | | |\n",
    "|  $\\mathbf{X}$   | training example matrix | `X_train` |\n",
    "|  $\\mathbf{y}$   | training example targets | `y_train` |\n",
    "| $\\mathbf{x}^{(i)}$, $y^{(i)}$ | $i_{th}$ Training Example | `X[i]`, `y[i]` |\n",
    "|        $m$       | number of training examples | `m` |\n",
    "|        $n$       | number of features in each example | `n` |\n",
    "|  $\\mathbf{w}$   | parameter: weight | `w` |\n",
    "|        $b$       | parameter: bias | `b` |\n",
    "| $f_{\\mathbf{w},b}(\\mathbf{x}^{(i)})$ | The result of the Model evaluation at $\\mathbf{x}^{(i)}$ parameterized by $\\mathbf{w},b$: $f_{\\mathbf{w},b}(\\mathbf{x}^{(i)}) = \\mathbf{w} \\cdot \\mathbf{x}^{(i)}+b$ | `f_wb` |\n",
    "| $\\frac{\\partial J(\\mathbf{w},b)}{\\partial w_j}$ | the gradient or partial derivative of cost with respect to parameter $w_j$ | `dj_dw[j]` |\n",
    "| $\\frac{\\partial J(\\mathbf{w},b)}{\\partial b}$ | the gradient or partial derivative of cost with respect to parameter $b$ | `dj_db` |\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fdd8f2b7",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "#  Problem Statement\n",
    "\n",
    "As in the previous labs, you will use the motivating example of housing price prediction. The training data set contains many examples with 4 features (size, bedrooms, floors and age) shown in the table below. Note, in this lab, the Size feature is in sqft while earlier labs utilized 1000 sqft.  This data set is larger than the previous lab.\n",
    "\n",
    "We would like to build a linear regression model using these values so we can then predict the price for other houses - say, a house with 1200 sqft, 3 bedrooms, 1 floor, 40 years old. \n",
    "\n",
    "##  Dataset: \n",
    "| Size (sqft) | Number of Bedrooms  | Number of floors | Age of  Home | Price (1000s dollars)  |   \n",
    "| ----------------| ------------------- |----------------- |--------------|----------------------- |  \n",
    "| 952             | 2                   | 1                | 65           | 271.5                  |  \n",
    "| 1244            | 3                   | 2                | 64           | 232                    |  \n",
    "| 1947            | 3                   | 2                | 17           | 509.8                  |  \n",
    "| ...             | ...                 | ...              | ...          | ...                    |\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "5cd0a677",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# load the dataset\n",
    "X_train, y_train = load_house_data()\n",
    "X_features = ['size(sqft)','bedrooms','floors','age']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cfaef490",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Let's view the dataset and its features by plotting each feature versus price."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "67ce47a7",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x216 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=plt.subplots(1, 4, figsize=(12, 3), sharey=True)\n",
    "for i in range(len(ax)):\n",
    "    ax[i].scatter(X_train[:,i],y_train)\n",
    "    ax[i].set_xlabel(X_features[i])\n",
    "ax[0].set_ylabel(\"Price (1000's)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38b16741",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Plotting each feature vs. the target, price, provides some indication of which features have the strongest influence on price. Above, increasing size also increases price. Bedrooms and floors don't seem to have a strong impact on price. Newer houses have higher prices than older houses."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0dfe1e9b",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "<a name=\"toc_15456_5\"></a>\n",
    "## Gradient Descent With Multiple Variables\n",
    "Here are the equations you developed in the last lab on gradient descent for multiple variables.:\n",
    "\n",
    "$$\\begin{align*} \\text{repeat}&\\text{ until convergence:} \\; \\lbrace \\newline\\;\n",
    "& w_j := w_j -  \\alpha \\frac{\\partial J(\\mathbf{w},b)}{\\partial w_j} \\tag{1}  \\; & \\text{for j = 0..n-1}\\newline\n",
    "&b\\ \\ := b -  \\alpha \\frac{\\partial J(\\mathbf{w},b)}{\\partial b}  \\newline \\rbrace\n",
    "\\end{align*}$$\n",
    "\n",
    "where, n is the number of features, parameters $w_j$,  $b$, are updated simultaneously and where  \n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\frac{\\partial J(\\mathbf{w},b)}{\\partial w_j}  &= \\frac{1}{m} \\sum\\limits_{i = 0}^{m-1} (f_{\\mathbf{w},b}(\\mathbf{x}^{(i)}) - y^{(i)})x_{j}^{(i)} \\tag{2}  \\\\\n",
    "\\frac{\\partial J(\\mathbf{w},b)}{\\partial b}  &= \\frac{1}{m} \\sum\\limits_{i = 0}^{m-1} (f_{\\mathbf{w},b}(\\mathbf{x}^{(i)}) - y^{(i)}) \\tag{3}\n",
    "\\end{align}\n",
    "$$\n",
    "* m is the number of training examples in the data set\n",
    "\n",
    "    \n",
    "*  $f_{\\mathbf{w},b}(\\mathbf{x}^{(i)})$ is the model's prediction, while $y^{(i)}$ is the target value\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a921fb4d",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Learning Rate\n",
    "<figure>\n",
    "    <img src=\"./images/C1_W2_Lab06_learningrate.PNG\" style=\"width:1200px;\" >\n",
    "</figure>\n",
    "The lectures discussed some of the issues related to setting the learning rate $\\alpha$. The learning rate controls the size of the update to the parameters. See equation (1) above. It is shared by all the parameters.  \n",
    "\n",
    "Let's run gradient descent and try a few settings of $\\alpha$ on our data set"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9df8e8a1",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### $\\alpha$ = 9.9e-7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "fe34ec81",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration Cost          w0       w1       w2       w3       b       djdw0    djdw1    djdw2    djdw3    djdb  \n",
      "---------------------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|\n",
      "        0 9.55884e+04  5.5e-01  1.0e-03  5.1e-04  1.2e-02  3.6e-04 -5.5e+05 -1.0e+03 -5.2e+02 -1.2e+04 -3.6e+02\n",
      "        1 1.28213e+05 -8.8e-02 -1.7e-04 -1.0e-04 -3.4e-03 -4.8e-05  6.4e+05  1.2e+03  6.2e+02  1.6e+04  4.1e+02\n",
      "        2 1.72159e+05  6.5e-01  1.2e-03  5.9e-04  1.3e-02  4.3e-04 -7.4e+05 -1.4e+03 -7.0e+02 -1.7e+04 -4.9e+02\n",
      "        3 2.31358e+05 -2.1e-01 -4.0e-04 -2.3e-04 -7.5e-03 -1.2e-04  8.6e+05  1.6e+03  8.3e+02  2.1e+04  5.6e+02\n",
      "        4 3.11100e+05  7.9e-01  1.4e-03  7.1e-04  1.5e-02  5.3e-04 -1.0e+06 -1.8e+03 -9.5e+02 -2.3e+04 -6.6e+02\n",
      "        5 4.18517e+05 -3.7e-01 -7.1e-04 -4.0e-04 -1.3e-02 -2.1e-04  1.2e+06  2.1e+03  1.1e+03  2.8e+04  7.5e+02\n",
      "        6 5.63212e+05  9.7e-01  1.7e-03  8.7e-04  1.8e-02  6.6e-04 -1.3e+06 -2.5e+03 -1.3e+03 -3.1e+04 -8.8e+02\n",
      "        7 7.58122e+05 -5.8e-01 -1.1e-03 -6.2e-04 -1.9e-02 -3.4e-04  1.6e+06  2.9e+03  1.5e+03  3.8e+04  1.0e+03\n",
      "        8 1.02068e+06  1.2e+00  2.2e-03  1.1e-03  2.3e-02  8.3e-04 -1.8e+06 -3.3e+03 -1.7e+03 -4.2e+04 -1.2e+03\n",
      "        9 1.37435e+06 -8.7e-01 -1.7e-03 -9.1e-04 -2.7e-02 -5.2e-04  2.1e+06  3.9e+03  2.0e+03  5.1e+04  1.4e+03\n",
      "w,b found by gradient descent: w: [-0.87 -0.   -0.   -0.03], b: -0.00\n"
     ]
    }
   ],
   "source": [
    "#set alpha to 9.9e-7\n",
    "_, _, hist = run_gradient_descent(X_train, y_train, 10, alpha = 9.9e-7)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c96a1c4e",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "It appears the learning rate is too high.  The solution does not converge. Cost is *increasing* rather than decreasing. Let's plot the result:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ff78ed91",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_cost_i_w(X_train, y_train, hist)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c07313a8",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "The plot on the right shows the value of one of the parameters, $w_0$. At each iteration, it is overshooting the optimal value and as a result, cost ends up *increasing* rather than approaching the minimum. Note that this is not a completely accurate picture as there are 4 parameters being modified each pass rather than just one. This plot is only showing $w_0$ with the other parameters fixed at benign values. In this and later plots you may notice the blue and orange lines being slightly off."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b6ace86",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "\n",
    "### $\\alpha$ = 9e-7\n",
    "Let's try a bit smaller value and see what happens."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "32fe697a",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration Cost          w0       w1       w2       w3       b       djdw0    djdw1    djdw2    djdw3    djdb  \n",
      "---------------------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|\n",
      "        0 6.64616e+04  5.0e-01  9.1e-04  4.7e-04  1.1e-02  3.3e-04 -5.5e+05 -1.0e+03 -5.2e+02 -1.2e+04 -3.6e+02\n",
      "        1 6.18990e+04  1.8e-02  2.1e-05  2.0e-06 -7.9e-04  1.9e-05  5.3e+05  9.8e+02  5.2e+02  1.3e+04  3.4e+02\n",
      "        2 5.76572e+04  4.8e-01  8.6e-04  4.4e-04  9.5e-03  3.2e-04 -5.1e+05 -9.3e+02 -4.8e+02 -1.1e+04 -3.4e+02\n",
      "        3 5.37137e+04  3.4e-02  3.9e-05  2.8e-06 -1.6e-03  3.8e-05  4.9e+05  9.1e+02  4.8e+02  1.2e+04  3.2e+02\n",
      "        4 5.00474e+04  4.6e-01  8.2e-04  4.1e-04  8.0e-03  3.2e-04 -4.8e+05 -8.7e+02 -4.5e+02 -1.1e+04 -3.1e+02\n",
      "        5 4.66388e+04  5.0e-02  5.6e-05  2.5e-06 -2.4e-03  5.6e-05  4.6e+05  8.5e+02  4.5e+02  1.2e+04  2.9e+02\n",
      "        6 4.34700e+04  4.5e-01  7.8e-04  3.8e-04  6.4e-03  3.2e-04 -4.4e+05 -8.1e+02 -4.2e+02 -9.8e+03 -2.9e+02\n",
      "        7 4.05239e+04  6.4e-02  7.0e-05  1.2e-06 -3.3e-03  7.3e-05  4.3e+05  7.9e+02  4.2e+02  1.1e+04  2.7e+02\n",
      "        8 3.77849e+04  4.4e-01  7.5e-04  3.5e-04  4.9e-03  3.2e-04 -4.1e+05 -7.5e+02 -3.9e+02 -9.1e+03 -2.7e+02\n",
      "        9 3.52385e+04  7.7e-02  8.3e-05 -1.1e-06 -4.2e-03  8.9e-05  4.0e+05  7.4e+02  3.9e+02  1.0e+04  2.5e+02\n",
      "w,b found by gradient descent: w: [ 7.74e-02  8.27e-05 -1.06e-06 -4.20e-03], b: 0.00\n"
     ]
    }
   ],
   "source": [
    "#set alpha to 9e-7\n",
    "_,_,hist = run_gradient_descent(X_train, y_train, 10, alpha = 9e-7)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3cda1a4b",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Cost is decreasing throughout the run showing that alpha is not too large. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e382eef0",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_cost_i_w(X_train, y_train, hist)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9abda677",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "On the left, you see that cost is decreasing as it should. On the right, you can see that $w_0$ is still oscillating around the minimum, but it is decreasing each iteration rather than increasing. Note above that `dj_dw[0]` changes sign with each iteration as `w[0]` jumps over the optimal value.\n",
    "This alpha value will converge. You can vary the number of iterations to see how it behaves."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88161797",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### $\\alpha$ = 1e-7\n",
    "Let's try a bit smaller value for $\\alpha$ and see what happens."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ba5eaaab",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration Cost          w0       w1       w2       w3       b       djdw0    djdw1    djdw2    djdw3    djdb  \n",
      "---------------------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|\n",
      "        0 4.42313e+04  5.5e-02  1.0e-04  5.2e-05  1.2e-03  3.6e-05 -5.5e+05 -1.0e+03 -5.2e+02 -1.2e+04 -3.6e+02\n",
      "        1 2.76461e+04  9.8e-02  1.8e-04  9.2e-05  2.2e-03  6.5e-05 -4.3e+05 -7.9e+02 -4.0e+02 -9.5e+03 -2.8e+02\n",
      "        2 1.75102e+04  1.3e-01  2.4e-04  1.2e-04  2.9e-03  8.7e-05 -3.4e+05 -6.1e+02 -3.1e+02 -7.3e+03 -2.2e+02\n",
      "        3 1.13157e+04  1.6e-01  2.9e-04  1.5e-04  3.5e-03  1.0e-04 -2.6e+05 -4.8e+02 -2.4e+02 -5.6e+03 -1.8e+02\n",
      "        4 7.53002e+03  1.8e-01  3.3e-04  1.7e-04  3.9e-03  1.2e-04 -2.1e+05 -3.7e+02 -1.9e+02 -4.2e+03 -1.4e+02\n",
      "        5 5.21639e+03  2.0e-01  3.5e-04  1.8e-04  4.2e-03  1.3e-04 -1.6e+05 -2.9e+02 -1.5e+02 -3.1e+03 -1.1e+02\n",
      "        6 3.80242e+03  2.1e-01  3.8e-04  1.9e-04  4.5e-03  1.4e-04 -1.3e+05 -2.2e+02 -1.1e+02 -2.3e+03 -8.6e+01\n",
      "        7 2.93826e+03  2.2e-01  3.9e-04  2.0e-04  4.6e-03  1.4e-04 -9.8e+04 -1.7e+02 -8.6e+01 -1.7e+03 -6.8e+01\n",
      "        8 2.41013e+03  2.3e-01  4.1e-04  2.1e-04  4.7e-03  1.5e-04 -7.7e+04 -1.3e+02 -6.5e+01 -1.2e+03 -5.4e+01\n",
      "        9 2.08734e+03  2.3e-01  4.2e-04  2.1e-04  4.8e-03  1.5e-04 -6.0e+04 -1.0e+02 -4.9e+01 -7.5e+02 -4.3e+01\n",
      "w,b found by gradient descent: w: [2.31e-01 4.18e-04 2.12e-04 4.81e-03], b: 0.00\n"
     ]
    }
   ],
   "source": [
    "#set alpha to 1e-7\n",
    "_,_,hist = run_gradient_descent(X_train, y_train, 10, alpha = 1e-7)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cede2ab",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Cost is decreasing throughout the run showing that $\\alpha$ is not too large. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f94a757b",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_cost_i_w(X_train,y_train,hist)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d26e1d32",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "On the left, you see that cost is decreasing as it should. On the right you can see that $w_0$ is decreasing without crossing the minimum. Note above that `dj_w0` is negative throughout the run. This solution will also converge, though not quite as quickly as the previous example."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0097ccbf",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "tags": []
   },
   "source": [
    "## Feature Scaling \n",
    "<figure>\n",
    "    <img src=\"./images/C1_W2_Lab06_featurescalingheader.PNG\" style=\"width:1200px;\" >\n",
    "</figure>\n",
    "The lectures described the importance of rescaling the dataset so the features have a similar range.\n",
    "If you are interested in the details of why this is the case, click on the 'details' header below. If not, the section below will walk through an implementation of how to do feature scaling."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af7675c9",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "<details>\n",
    "<summary>\n",
    "    <font size='3', color='darkgreen'><b>Details</b></font>\n",
    "</summary>\n",
    "\n",
    "Let's look again at the situation with $\\alpha$ = 9e-7. This is pretty close to the maximum value we can set $\\alpha$  to without diverging. This is a short run showing the first few iterations:\n",
    "\n",
    "<figure>\n",
    "    <img src=\"./images/C1_W2_Lab06_ShortRun.PNG\" style=\"width:1200px;\" >\n",
    "</figure>\n",
    "\n",
    "Above, while cost is being decreased, its clear that $w_0$ is making more rapid progress than the other parameters due to its much larger gradient.\n",
    "\n",
    "The graphic below shows the result of a very long run with $\\alpha$ = 9e-7. This takes several hours.\n",
    "\n",
    "<figure>\n",
    "    <img src=\"./images/C1_W2_Lab06_LongRun.PNG\" style=\"width:1200px;\" >\n",
    "</figure>\n",
    "    \n",
    "Above, you can see cost decreased slowly after its initial reduction. Notice the difference between `w0` and `w1`,`w2`,`w3` as well as  `dj_dw0` and `dj_dw1-3`. `w0` reaches its near final value very quickly and `dj_dw0` has quickly decreased to a small value showing that `w0` is near the final value. The other parameters were reduced much more slowly.\n",
    "\n",
    "Why is this?  Is there something we can improve? See below:\n",
    "<figure>\n",
    "    <center> <img src=\"./images/C1_W2_Lab06_scale.PNG\"   ></center>\n",
    "</figure>   \n",
    "\n",
    "The figure above shows why $w$'s are updated unevenly. \n",
    "- $\\alpha$ is shared by all parameter updates ($w$'s and $b$).\n",
    "- the common error term is multiplied by the features for the $w$'s. (not $b$).\n",
    "- the features vary significantly in magnitude making some features update much faster than others. In this case, $w_0$ is multiplied by 'size(sqft)', which is generally > 1000,  while $w_1$ is multiplied by 'number of bedrooms', which is generally 2-4. \n",
    "    \n",
    "The solution is Feature Scaling."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78a0d10d",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "The lectures discussed three different techniques: \n",
    "- Feature scaling, essentially dividing each positive feature by its maximum value, or more generally, rescale each feature by both its minimum and maximum values using (x-min)/(max-min). Both ways normalizes features to the range of -1 and 1, where the former method works for positive features which is simple and serves well for the lecture's example, and the latter method works for any features.\n",
    "- Mean normalization: $x_i := \\dfrac{x_i - \\mu_i}{max - min} $ \n",
    "- Z-score normalization which we will explore below. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e575998",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "\n",
    "### z-score normalization \n",
    "After z-score normalization, all features will have a mean of 0 and a standard deviation of 1.\n",
    "\n",
    "To implement z-score normalization, adjust your input values as shown in this formula:\n",
    "$$x^{(i)}_j = \\dfrac{x^{(i)}_j - \\mu_j}{\\sigma_j} \\tag{4}$$ \n",
    "where $j$ selects a feature or a column in the $\\mathbf{X}$ matrix. $µ_j$ is the mean of all the values for feature (j) and $\\sigma_j$ is the standard deviation of feature (j).\n",
    "$$\n",
    "\\begin{align}\n",
    "\\mu_j &= \\frac{1}{m} \\sum_{i=0}^{m-1} x^{(i)}_j \\tag{5}\\\\\n",
    "\\sigma^2_j &= \\frac{1}{m} \\sum_{i=0}^{m-1} (x^{(i)}_j - \\mu_j)^2  \\tag{6}\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    ">**Implementation Note:** When normalizing the features, it is important\n",
    "to store the values used for normalization - the mean value and the standard deviation used for the computations. After learning the parameters\n",
    "from the model, we often want to predict the prices of houses we have not\n",
    "seen before. Given a new x value (living room area and number of bed-\n",
    "rooms), we must first normalize x using the mean and standard deviation\n",
    "that we had previously computed from the training set.\n",
    "\n",
    "**Implementation**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e7b13d18",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "def zscore_normalize_features(X):\n",
    "    \"\"\"\n",
    "    computes  X, zcore normalized by column\n",
    "    \n",
    "    Args:\n",
    "      X (ndarray (m,n))     : input data, m examples, n features\n",
    "      \n",
    "    Returns:\n",
    "      X_norm (ndarray (m,n)): input normalized by column\n",
    "      mu (ndarray (n,))     : mean of each feature\n",
    "      sigma (ndarray (n,))  : standard deviation of each feature\n",
    "    \"\"\"\n",
    "    # find the mean of each column/feature\n",
    "    mu     = np.mean(X, axis=0)                 # mu will have shape (n,)\n",
    "    # find the standard deviation of each column/feature\n",
    "    sigma  = np.std(X, axis=0)                  # sigma will have shape (n,)\n",
    "    # element-wise, subtract mu for that column from each example, divide by std for that column\n",
    "    X_norm = (X - mu) / sigma      \n",
    "\n",
    "    return (X_norm, mu, sigma)\n",
    " \n",
    "#check our work\n",
    "#from sklearn.preprocessing import scale\n",
    "#scale(X_orig, axis=0, with_mean=True, with_std=True, copy=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d1fa01a",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Let's look at the steps involved in Z-score normalization. The plot below shows the transformation step by step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d64c9f63",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu     = np.mean(X_train,axis=0)   \n",
    "sigma  = np.std(X_train,axis=0) \n",
    "X_mean = (X_train - mu)\n",
    "X_norm = (X_train - mu)/sigma      \n",
    "\n",
    "fig,ax=plt.subplots(1, 3, figsize=(12, 3))\n",
    "ax[0].scatter(X_train[:,0], X_train[:,3])\n",
    "ax[0].set_xlabel(X_features[0]); ax[0].set_ylabel(X_features[3]);\n",
    "ax[0].set_title(\"unnormalized\")\n",
    "ax[0].axis('equal')\n",
    "\n",
    "ax[1].scatter(X_mean[:,0], X_mean[:,3])\n",
    "ax[1].set_xlabel(X_features[0]); ax[0].set_ylabel(X_features[3]);\n",
    "ax[1].set_title(r\"X - $\\mu$\")\n",
    "ax[1].axis('equal')\n",
    "\n",
    "ax[2].scatter(X_norm[:,0], X_norm[:,3])\n",
    "ax[2].set_xlabel(X_features[0]); ax[0].set_ylabel(X_features[3]);\n",
    "ax[2].set_title(r\"Z-score normalized\")\n",
    "ax[2].axis('equal')\n",
    "plt.tight_layout(rect=[0, 0.03, 1, 0.95])\n",
    "fig.suptitle(\"distribution of features before, during, after normalization\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51bdd057",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "The plot above shows the relationship between two of the training set parameters, \"age\" and \"size(sqft)\". *These are plotted with equal scale*. \n",
    "- Left: Unnormalized: The range of values or the variance of the 'size(sqft)' feature is much larger than that of age\n",
    "- Middle: The first step removes the mean or average value from each feature. This leaves features that are centered around zero. It's difficult to see the difference for the 'age' feature, but 'size(sqft)' is clearly around zero.\n",
    "- Right: The second step divides by the variance. This leaves both features centered at zero with a similar scale."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "995388bb",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Let's normalize the data and compare it to the original data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "592747d1",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X_mu = [1.42e+03 2.72e+00 1.38e+00 3.84e+01], \n",
      "X_sigma = [411.62   0.65   0.49  25.78]\n",
      "Peak to Peak range by column in Raw        X:[2.41e+03 4.00e+00 1.00e+00 9.50e+01]\n",
      "Peak to Peak range by column in Normalized X:[5.85 6.14 2.06 3.69]\n"
     ]
    }
   ],
   "source": [
    "# normalize the original features\n",
    "X_norm, X_mu, X_sigma = zscore_normalize_features(X_train)\n",
    "print(f\"X_mu = {X_mu}, \\nX_sigma = {X_sigma}\")\n",
    "print(f\"Peak to Peak range by column in Raw        X:{np.ptp(X_train,axis=0)}\")   \n",
    "print(f\"Peak to Peak range by column in Normalized X:{np.ptp(X_norm,axis=0)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08f2bffb",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "The peak to peak range of each column is reduced from a factor of thousands to a factor of 2-3 by normalization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "48c76052",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=plt.subplots(1, 4, figsize=(12, 3))\n",
    "for i in range(len(ax)):\n",
    "    norm_plot(ax[i],X_train[:,i],)\n",
    "    ax[i].set_xlabel(X_features[i])\n",
    "ax[0].set_ylabel(\"count\");\n",
    "fig.suptitle(\"distribution of features before normalization\")\n",
    "plt.show()\n",
    "fig,ax=plt.subplots(1,4,figsize=(12,3))\n",
    "for i in range(len(ax)):\n",
    "    norm_plot(ax[i],X_norm[:,i],)\n",
    "    ax[i].set_xlabel(X_features[i])\n",
    "ax[0].set_ylabel(\"count\"); \n",
    "fig.suptitle(\"distribution of features after normalization\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a95dde5a",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Notice, above, the range of the normalized data (x-axis) is centered around zero and roughly +/- 2. Most importantly, the range is similar for each feature."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae92414b",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Let's re-run our gradient descent algorithm with normalized data.\n",
    "Note the **vastly larger value of alpha**. This will speed up gradient descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "f22af96a",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration Cost          w0       w1       w2       w3       b       djdw0    djdw1    djdw2    djdw3    djdb  \n",
      "---------------------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|\n",
      "        0 5.76170e+04  8.9e+00  3.0e+00  3.3e+00 -6.0e+00  3.6e+01 -8.9e+01 -3.0e+01 -3.3e+01  6.0e+01 -3.6e+02\n",
      "      100 2.21086e+02  1.1e+02 -2.0e+01 -3.1e+01 -3.8e+01  3.6e+02 -9.2e-01  4.5e-01  5.3e-01 -1.7e-01 -9.6e-03\n",
      "      200 2.19209e+02  1.1e+02 -2.1e+01 -3.3e+01 -3.8e+01  3.6e+02 -3.0e-02  1.5e-02  1.7e-02 -6.0e-03 -2.6e-07\n",
      "      300 2.19207e+02  1.1e+02 -2.1e+01 -3.3e+01 -3.8e+01  3.6e+02 -1.0e-03  5.1e-04  5.7e-04 -2.0e-04 -6.9e-12\n",
      "      400 2.19207e+02  1.1e+02 -2.1e+01 -3.3e+01 -3.8e+01  3.6e+02 -3.4e-05  1.7e-05  1.9e-05 -6.6e-06 -2.7e-13\n",
      "      500 2.19207e+02  1.1e+02 -2.1e+01 -3.3e+01 -3.8e+01  3.6e+02 -1.1e-06  5.6e-07  6.2e-07 -2.2e-07 -2.7e-13\n",
      "      600 2.19207e+02  1.1e+02 -2.1e+01 -3.3e+01 -3.8e+01  3.6e+02 -3.7e-08  1.9e-08  2.1e-08 -7.3e-09 -2.6e-13\n",
      "      700 2.19207e+02  1.1e+02 -2.1e+01 -3.3e+01 -3.8e+01  3.6e+02 -1.2e-09  6.2e-10  6.9e-10 -2.4e-10 -2.6e-13\n",
      "      800 2.19207e+02  1.1e+02 -2.1e+01 -3.3e+01 -3.8e+01  3.6e+02 -4.1e-11  2.1e-11  2.3e-11 -8.1e-12 -2.6e-13\n",
      "      900 2.19207e+02  1.1e+02 -2.1e+01 -3.3e+01 -3.8e+01  3.6e+02 -1.4e-12  6.9e-13  7.7e-13 -2.7e-13 -2.6e-13\n",
      "w,b found by gradient descent: w: [110.56 -21.27 -32.71 -37.97], b: 363.16\n"
     ]
    }
   ],
   "source": [
    "w_norm, b_norm, hist = run_gradient_descent(X_norm, y_train, 1000, 1.0e-1, )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e20f2113",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "The scaled features get very accurate results **much, much faster!**. Notice the gradient of each parameter is tiny by the end of this fairly short run. A learning rate of 0.1 is a good start for regression with normalized features.\n",
    "Let's plot our predictions versus the target values. Note, the prediction is made using the normalized feature while the plot is shown using the original feature values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "31845003",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#predict target using normalized features\n",
    "m = X_norm.shape[0]\n",
    "yp = np.zeros(m)\n",
    "for i in range(m):\n",
    "    yp[i] = np.dot(X_norm[i], w_norm) + b_norm\n",
    "\n",
    "    # plot predictions and targets versus original features    \n",
    "fig,ax=plt.subplots(1,4,figsize=(12, 3),sharey=True)\n",
    "for i in range(len(ax)):\n",
    "    ax[i].scatter(X_train[:,i],y_train, label = 'target')\n",
    "    ax[i].set_xlabel(X_features[i])\n",
    "    ax[i].scatter(X_train[:,i],yp,color=dlc[\"dlorange\"], label = 'predict')\n",
    "ax[0].set_ylabel(\"Price\"); ax[0].legend();\n",
    "fig.suptitle(\"target versus prediction using z-score normalized model\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ad1d19c",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "The results look good. A few points to note:\n",
    "- with multiple features, we can no longer have a single plot showing results versus features.\n",
    "- when generating the plot, the normalized features were used. Any predictions using the parameters learned from a normalized training set must also be normalized."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adbe656f",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "**Prediction**\n",
    "The point of generating our model is to use it to predict housing prices that are not in the data set. Let's predict the price of a house with 1200 sqft, 3 bedrooms, 1 floor, 40 years old. Recall, that you must normalize the data with the mean and standard deviation derived when the training data was normalized. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "cb3b7235",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.53  0.43 -0.79  0.06]\n",
      " predicted price of a house with 1200 sqft, 3 bedrooms, 1 floor, 40 years old = $318709\n"
     ]
    }
   ],
   "source": [
    "# First, normalize out example.\n",
    "x_house = np.array([1200, 3, 1, 40])\n",
    "x_house_norm = (x_house - X_mu) / X_sigma\n",
    "print(x_house_norm)\n",
    "x_house_predict = np.dot(x_house_norm, w_norm) + b_norm\n",
    "print(f\" predicted price of a house with 1200 sqft, 3 bedrooms, 1 floor, 40 years old = ${x_house_predict*1000:0.0f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e723c598",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "**Cost Contours**  \n",
    "<img align=\"left\" src=\"./images/C1_W2_Lab06_contours.PNG\"   style=\"width:240px;\" >Another way to view feature scaling is in terms of the cost contours. When feature scales do not match, the plot of cost versus parameters in a contour plot is asymmetric. \n",
    "\n",
    "In the plot below, the scale of the parameters is matched. The left plot is the cost contour plot of w[0], the square feet versus w[1], the number of bedrooms before normalizing the features. The plot is so asymmetric, the curves completing the contours are not visible. In contrast, when the features are normalized, the cost contour is much more symmetric. The result is that updates to parameters during gradient descent can make equal progress for each parameter. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "f380b8f4",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt_equal_scale(X_train, X_norm, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18688194",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "\n",
    "## Congratulations!\n",
    "In this lab you:\n",
    "- utilized the routines for linear regression with multiple features you developed in previous labs\n",
    "- explored the impact of the learning rate  $\\alpha$ on convergence \n",
    "- discovered the value of feature scaling using z-score normalization in speeding convergence"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "755249cb",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Acknowledgments\n",
    "The housing data was derived from the [Ames Housing dataset](http://jse.amstat.org/v19n3/decock.pdf) compiled by Dean De Cock for use in data science education."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "01b8b18f",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.3"
  },
  "toc-autonumbering": false
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
